Questions from Calculus

Q: If a function has derivatives from both the right and the left

If a function has derivatives from both the right and the left at a point, then it is differentiable at that point.

Q: If a function is differentiable at a point, then it is

If a function is differentiable at a point, then it is continuous at that point.

Q: Let / and / Show that f is

Let and Show that f is continuous, but not differentiable, at x = 0. Show that g is differentiable at 0 and find g′(0).

Q: Find the slope of the tangent line to the graph of the

Find the slope of the tangent line to the graph of the function at the given point. f(t) = 3t − t2, (0, 0)

Q: Use a graphing utility to graph the two functions f(x

Use a graphing utility to graph the two functions f(x) = x2 + 1 and g(x) = │x│ + 1 in the same viewing window. Use the zoom and trace features to analyze the graphs near the point (0, 1). What do you...

Q: Describe the relationship between pre-calculus and calculus. List three

Describe the relationship between pre-calculus and calculus. List three pre-calculus concepts and their corresponding calculus counterparts.

Q: Discuss the relationship between secant lines through a fixed point and a

Discuss the relationship between secant lines through a fixed point and a corresponding tangent line at that fixed point.

Q: Decide whether the problem can be solved using pre-calculus or

Decide whether the problem can be solved using pre-calculus or whether calculus is required. If the problem can be solved using pre-calculus, solve it. If the problem seems to require calculus, explai...

Q: Decide whether the problem can be solved using pre-calculus or

Decide whether the problem can be solved using pre-calculus or whether calculus is required. If the problem can be solved using pre-calculus, solve it. If the problem seems to require calculus, explai...

Q: A bicyclist is riding on a path modeled by the function f

A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x − x2), where x and f(x) are measured in miles (see figure). Find the rate of change of elevation at x = 2.